Block #15,661

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 8:08:07 PM · Difficulty 7.8573 · 6,792,769 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c798b1dbc7b8f6181714e59090f2cbfcdff05e67fdd32b86d3b91ed55597c62a

View on Chainz ↗

Height

#15,661

Difficulty

7.857320

Transactions

Size

428 B

Version

Bits

07db794b

Nonce

198

Timestamp

7/11/2013, 8:08:07 PM

Confirmations

6,792,769

Mined by

⛏️ P2SHAayVX9odA9ZtzgCi99Sh4XSQLE1xiVTMQW

Merkle Root

71ab7a0e9ebcb4826c4472eb7f6e86120229e142f5fc7137142066969c975b00

Transactions (2)

Coinbasecc6181f40d5650…7d4b935d8df9ab

1 in → 1 out16.1900 XPM108 B

AayVX9od…1xiVTMQW

71c2a0a5e62212…2349eb868a76d9

1 in → 2 out16.9100 XPM226 B

AJvQE1xd…3qwCLTd1 AbKXiYgC…afBu1Lxa

Prime Chain Origin

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

3.430 × 10¹⁰⁵(106-digit number)

34301927678946075303…30232517412701026939

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

3.430 × 10¹⁰⁵(106-digit number)

34301927678946075303…30232517412701026939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.430 × 10¹⁰⁵(106-digit number)

34301927678946075303…30232517412701026941

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

6.860 × 10¹⁰⁵(106-digit number)

68603855357892150607…60465034825402053879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.860 × 10¹⁰⁵(106-digit number)

68603855357892150607…60465034825402053881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.372 × 10¹⁰⁶(107-digit number)

13720771071578430121…20930069650804107759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.372 × 10¹⁰⁶(107-digit number)

13720771071578430121…20930069650804107761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.744 × 10¹⁰⁶(107-digit number)

27441542143156860242…41860139301608215519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #15,661

Cookie Preferences