Block #361,911

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/16/2014, 9:20:53 AM · Difficulty 10.4092 · 6,432,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd17bd3401e5628aa8bbe504dbdb20f7afaee546bc89c42a0ee0d911a1e8ac33

View on Chainz ↗

Height

#361,911

Difficulty

10.409208

Transactions

Size

458 B

Version

Bits

0a68c1e3

Nonce

68,132

Timestamp

1/16/2014, 9:20:53 AM

Confirmations

6,432,552

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

1ac10c7627ef521b033181c81ba53f7a45b4544d19ee34f16c79b5f335c54f95

Transactions (2)

Coinbasecd7c415614242d…78a4683c04afa8

1 in → 2 out9.2200 XPM137 B

ARmAMwyu…P7Kn74ZT ALfEGCwh…VawujfMm

7126502093c206…13c1b3a5264d3c

1 in → 2 out253.3074 XPM227 B

AT4s23n2…RL4dV7QK Ads3fmji…fG9sCNZ9

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.

1.454 × 10¹⁰⁵(106-digit number)

14544984462807258517…86321763508423423999

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

1.454 × 10¹⁰⁵(106-digit number)

14544984462807258517…86321763508423423999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.454 × 10¹⁰⁵(106-digit number)

14544984462807258517…86321763508423424001

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

2.908 × 10¹⁰⁵(106-digit number)

29089968925614517034…72643527016846847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.908 × 10¹⁰⁵(106-digit number)

29089968925614517034…72643527016846848001

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

5.817 × 10¹⁰⁵(106-digit number)

58179937851229034069…45287054033693695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.817 × 10¹⁰⁵(106-digit number)

58179937851229034069…45287054033693696001

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

1.163 × 10¹⁰⁶(107-digit number)

11635987570245806813…90574108067387391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.163 × 10¹⁰⁶(107-digit number)

11635987570245806813…90574108067387392001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.327 × 10¹⁰⁶(107-digit number)

23271975140491613627…81148216134774783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.327 × 10¹⁰⁶(107-digit number)

23271975140491613627…81148216134774784001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.654 × 10¹⁰⁶(107-digit number)

46543950280983227255…62296432269549567999

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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