Block #2,131,362

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/25/2017, 1:29:09 AM · Difficulty 10.9101 · 4,709,693 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1df8a35ff7214995620d9d7ddb57cfd11a13edf6d0e439aed3fdafb432af7a84

View on Chainz ↗

Height

#2,131,362

Difficulty

10.910085

Transactions

Size

879 B

Version

Bits

0ae8fb5b

Nonce

765,655,267

Timestamp

5/25/2017, 1:29:09 AM

Confirmations

4,709,693

Mined by

⛏️ P2SHAeB463YNEDkBzt2JCdpjFbm5f49X6sn58u

Merkle Root

07f992a6282674984feb878f63a7cbf9c97336b84f0ecc817810f1b6309d4e42

Transactions (4)

Coinbasefc8b26d1431c10…a22dc2e16a4901

1 in → 1 out8.4200 XPM109 B

AeB463YN…9X6sn58u

0f27067429c806…40df67ee7f8182

1 in → 2 out179151.6585 XPM226 B

AY5ZHEwJ…HzDe3fup AN1EGxhR…uTWDBrmn

0d1a6a43e3bdd2…12f38d16307fe0

1 in → 2 out51795.7340 XPM226 B

APe7MFxP…LWenBVYt ANoevYiU…D6vvpbK5

54701f999f46e4…410964f1c828f8

1 in → 2 out51789.9063 XPM227 B

Abcd8fen…pxss3PDa AHKTfTWq…ZgNSzCsE

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.

4.200 × 10⁹⁶(97-digit number)

42004699031477457058…59568016799387238399

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

4.200 × 10⁹⁶(97-digit number)

42004699031477457058…59568016799387238399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.200 × 10⁹⁶(97-digit number)

42004699031477457058…59568016799387238401

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

8.400 × 10⁹⁶(97-digit number)

84009398062954914116…19136033598774476799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.400 × 10⁹⁶(97-digit number)

84009398062954914116…19136033598774476801

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

1.680 × 10⁹⁷(98-digit number)

16801879612590982823…38272067197548953599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.680 × 10⁹⁷(98-digit number)

16801879612590982823…38272067197548953601

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

3.360 × 10⁹⁷(98-digit number)

33603759225181965646…76544134395097907199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.360 × 10⁹⁷(98-digit number)

33603759225181965646…76544134395097907201

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

6.720 × 10⁹⁷(98-digit number)

67207518450363931293…53088268790195814399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.720 × 10⁹⁷(98-digit number)

67207518450363931293…53088268790195814401

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

1.344 × 10⁹⁸(99-digit number)

13441503690072786258…06176537580391628799

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

Block #2,131,362

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