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Block #771,699

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/17/2014, 12:18:04 AM Β· Difficulty 10.9812 Β· 6,039,449 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
c88e0b3dd6c096eeec90770d905602db45e059914e0cdaf59261a217087dc7bf
View on Chainz β†—

Height

#771,699

Difficulty

10.981153

Transactions

2

Size

3.74 KB

Version

2

Bits

0afb2cd9

Nonce

1,614,152,507

Timestamp

10/17/2014, 12:18:04 AM

Confirmations

6,039,449

Mined by

⛏️ P2SHASQS81pE6AMWGeHpsyFBzRUhjN6ZGSG1c4

Merkle Root

0ebb9e31fcc73ddcafbc66e230a5b6269e87bc25201f39eeb7791722f601b002
Transactions (2)
Coinbase8080c72f67ef0f…1647adde471a23
1 in β†’ 1 out8.3200 XPM110 B
ASQS81pE…6ZGSG1c4
91ec5e56ce1a23…7e6dd3a40fc8e8
24 in β†’ 2 out100.0000 XPM3.54 KB
AdvgqtF9…vPXFaVVwAaK6svE2…KPgwVRuS
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.879 Γ— 10⁹⁢(97-digit number)
18794165559141687107…59243315757399654399
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.879 Γ— 10⁹⁢(97-digit number)
18794165559141687107…59243315757399654399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.879 Γ— 10⁹⁢(97-digit number)
18794165559141687107…59243315757399654401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.758 Γ— 10⁹⁢(97-digit number)
37588331118283374215…18486631514799308799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.758 Γ— 10⁹⁢(97-digit number)
37588331118283374215…18486631514799308801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
7.517 Γ— 10⁹⁢(97-digit number)
75176662236566748430…36973263029598617599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.517 Γ— 10⁹⁢(97-digit number)
75176662236566748430…36973263029598617601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.503 Γ— 10⁹⁷(98-digit number)
15035332447313349686…73946526059197235199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.503 Γ— 10⁹⁷(98-digit number)
15035332447313349686…73946526059197235201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.007 Γ— 10⁹⁷(98-digit number)
30070664894626699372…47893052118394470399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.007 Γ— 10⁹⁷(98-digit number)
30070664894626699372…47893052118394470401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.014 Γ— 10⁹⁷(98-digit number)
60141329789253398744…95786104236788940799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,733,294 XPMΒ·at block #6,811,147 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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