Block #155,676

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 11:58:16 AM · Difficulty 9.8659 · 6,646,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e017b7c7e255957c4d412196144b9cf6cc1aaa8fbdb6ae9baf8a5c8c34110f3a

View on Chainz ↗

Height

#155,676

Difficulty

9.865931

Transactions

Size

1.01 KB

Version

Bits

09ddadae

Nonce

34,563

Timestamp

9/8/2013, 11:58:16 AM

Confirmations

6,646,137

Mined by

⛏️ P2SHAZGUEaLumt5EXmysuYEo2bfzueCeY3dZTn

Merkle Root

2d9d040fd712e785b3bfbf790a6e34a32e19d2aadf14b1ae20370a4c3027ac23

Transactions (3)

Coinbasebac64addf9e9c7…ce8b1254d5b922

1 in → 1 out10.2800 XPM109 B

AZGUEaLu…CeY3dZTn

6a0ff6f16422fd…a35a5c1a1c092b

5 in → 1 out51.5500 XPM612 B

AZXqJQeh…qXkqXLDq

e9e2f59c109ef5…d1abbc84e79ba6

1 in → 2 out2.2009 XPM226 B

ATV6ek4M…eLXDWHBH AMRnMSro…uq9bMMmU

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.

2.412 × 10⁹²(93-digit number)

24124845686448646113…97366988085091622359

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

2.412 × 10⁹²(93-digit number)

24124845686448646113…97366988085091622359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.412 × 10⁹²(93-digit number)

24124845686448646113…97366988085091622361

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

4.824 × 10⁹²(93-digit number)

48249691372897292226…94733976170183244719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.824 × 10⁹²(93-digit number)

48249691372897292226…94733976170183244721

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

9.649 × 10⁹²(93-digit number)

96499382745794584453…89467952340366489439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.649 × 10⁹²(93-digit number)

96499382745794584453…89467952340366489441

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

1.929 × 10⁹³(94-digit number)

19299876549158916890…78935904680732978879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.929 × 10⁹³(94-digit number)

19299876549158916890…78935904680732978881

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

3.859 × 10⁹³(94-digit number)

38599753098317833781…57871809361465957759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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