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Block #1,667,641

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/10/2016, 11:33:37 PM Β· Difficulty 10.6979 Β· 5,177,573 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d72e6ee588258e2572ec12178f5edf72a17cd366d2789e1174e94cbc52c0780c
View on Chainz β†—

Height

#1,667,641

Difficulty

10.697893

Transactions

1

Size

199 B

Version

2

Bits

0ab2a925

Nonce

698,731,655

Timestamp

7/10/2016, 11:33:37 PM

Confirmations

5,177,573

Mined by

⛏️ P2SHAY6nwbRSrntcfPJnma9kiXqSfX5LfUE9cu

Merkle Root

9b5d18b27d189fd3556e29eb47477155d86f13021246a528e4cec4b088874ecb
Transactions (1)
Coinbase9b5d18b27d189f…cec4b088874ecb
1 in β†’ 1 out8.7200 XPM109 B
AY6nwbRS…5LfUE9cu
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.

7.134 Γ— 10⁹³(94-digit number)
71342695689621710810…59131993617708438899
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
7.134 Γ— 10⁹³(94-digit number)
71342695689621710810…59131993617708438899
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.134 Γ— 10⁹³(94-digit number)
71342695689621710810…59131993617708438901
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
1.426 Γ— 10⁹⁴(95-digit number)
14268539137924342162…18263987235416877799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.426 Γ— 10⁹⁴(95-digit number)
14268539137924342162…18263987235416877801
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
2.853 Γ— 10⁹⁴(95-digit number)
28537078275848684324…36527974470833755599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.853 Γ— 10⁹⁴(95-digit number)
28537078275848684324…36527974470833755601
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
5.707 Γ— 10⁹⁴(95-digit number)
57074156551697368648…73055948941667511199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.707 Γ— 10⁹⁴(95-digit number)
57074156551697368648…73055948941667511201
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
1.141 Γ— 10⁹⁡(96-digit number)
11414831310339473729…46111897883335022399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.141 Γ— 10⁹⁡(96-digit number)
11414831310339473729…46111897883335022401
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:58,006,145 XPMΒ·at block #6,845,213 Β· updates every 60s
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