Block #2,137,299

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/29/2017, 10:23:40 PM · Difficulty 10.8889 · 4,671,262 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

227fb552a7bbc309c803510621b4f39ca73fadd9dd7525f18e567b20913350c6

View on Chainz ↗

Height

#2,137,299

Difficulty

10.888913

Transactions

Size

1019 B

Version

Bits

0ae38fd4

Nonce

1,097,823,092

Timestamp

5/29/2017, 10:23:40 PM

Confirmations

4,671,262

Mined by

⛏️ P2SHAbk7wFwh7kJQRp7qxscEbWwYgD2APvKKQx

Merkle Root

1f2f68d3c3d2b07f0410079ff479a43ed6bcd8fbdb59feaec5114f7e48afb6b7

Transactions (2)

Coinbase2468489060c79b…12a8777c1db95d

1 in → 1 out8.4600 XPM110 B

Abk7wFwh…2APvKKQx

9afb8efd304edf…cb1f7a0e067a08

5 in → 2 out7384.6159 XPM818 B

ASiMNLCH…iCCjQWkw Ada1dx2w…8gd1gZg2

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.

2.416 × 10⁹⁷(98-digit number)

24164143624193762219…65772229759766855679

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

2.416 × 10⁹⁷(98-digit number)

24164143624193762219…65772229759766855679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.416 × 10⁹⁷(98-digit number)

24164143624193762219…65772229759766855681

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

4.832 × 10⁹⁷(98-digit number)

48328287248387524439…31544459519533711359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.832 × 10⁹⁷(98-digit number)

48328287248387524439…31544459519533711361

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

9.665 × 10⁹⁷(98-digit number)

96656574496775048879…63088919039067422719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.665 × 10⁹⁷(98-digit number)

96656574496775048879…63088919039067422721

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

1.933 × 10⁹⁸(99-digit number)

19331314899355009775…26177838078134845439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.933 × 10⁹⁸(99-digit number)

19331314899355009775…26177838078134845441

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

3.866 × 10⁹⁸(99-digit number)

38662629798710019551…52355676156269690879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.866 × 10⁹⁸(99-digit number)

38662629798710019551…52355676156269690881

Verify on FactorDB ↗Wolfram Alpha ↗

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

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 — 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

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 × 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 #2,137,299

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