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Block #1,714,255

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/12/2016, 7:55:42 PM Β· Difficulty 10.6555 Β· 5,116,810 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b12bcf4a9e187da04d11c1608e24cb6cf08f0ddb9054c5b65fc982da4d73003
View on Chainz β†—

Height

#1,714,255

Difficulty

10.655466

Transactions

1

Size

243 B

Version

2

Bits

0aa7cc9e

Nonce

86,713,876

Timestamp

8/12/2016, 7:55:42 PM

Confirmations

5,116,810

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

a150cde4642a0277950b41b6616079ea8fb1be83b0cdf7dad89958c45ec63cd0
Transactions (1)
Coinbasea150cde4642a02…9958c45ec63cd0
1 in β†’ 2 out8.7900 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

2.187 Γ— 10⁹⁷(98-digit number)
21877737778658502137…39839166495395430399
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
2.187 Γ— 10⁹⁷(98-digit number)
21877737778658502137…39839166495395430399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.187 Γ— 10⁹⁷(98-digit number)
21877737778658502137…39839166495395430401
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
4.375 Γ— 10⁹⁷(98-digit number)
43755475557317004275…79678332990790860799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.375 Γ— 10⁹⁷(98-digit number)
43755475557317004275…79678332990790860801
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
8.751 Γ— 10⁹⁷(98-digit number)
87510951114634008551…59356665981581721599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.751 Γ— 10⁹⁷(98-digit number)
87510951114634008551…59356665981581721601
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
1.750 Γ— 10⁹⁸(99-digit number)
17502190222926801710…18713331963163443199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.750 Γ— 10⁹⁸(99-digit number)
17502190222926801710…18713331963163443201
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
3.500 Γ— 10⁹⁸(99-digit number)
35004380445853603420…37426663926326886399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.500 Γ— 10⁹⁸(99-digit number)
35004380445853603420…37426663926326886401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,892,659 XPMΒ·at block #6,831,064 Β· updates every 60s
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