Block #237,542

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 2:40:58 AM · Difficulty 9.9499 · 6,573,082 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b66d5cf0b2b21e53357d9de16685e21f65b84febeecd1325a00eb36d648ac439

View on Chainz ↗

Height

#237,542

Difficulty

9.949908

Transactions

Size

1.72 KB

Version

Bits

09f32d2a

Nonce

4,397

Timestamp

11/1/2013, 2:40:58 AM

Confirmations

6,573,082

Mined by

⛏️ P2SHAaC7FfYJ3wgrxGC78ZvTmB5mToNd6BeiX3

Merkle Root

adbc2ebcf13b50b69ba747cec6b79440ca94fcf6440c950174be66319164e2a1

Transactions (4)

Coinbase7ed976b1265efe…907a0035d38424

1 in → 1 out10.1300 XPM109 B

AaC7FfYJ…Nd6BeiX3

bd53602fa01e8e…8c2de22a54f7b6

3 in → 2 out1520.9100 XPM520 B

AUXQqgZY…moyhtRYs Ac7RAQMV…nKWU2GLU

fbc79883a1f899…369bb4a3c0cf98

1 in → 2 out10.0900 XPM225 B

ARskhKeb…UgDvvX9P AaebCKa6…vowyh4cK

e45412aadcf191…9b2e96f21cbdd4

5 in → 2 out2.0479 XPM817 B

AbgUN6op…erPpCsqb AJv5WoqT…tqCRQqFk

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.

6.744 × 10¹⁰²(103-digit number)

67440639685042186984…29218718501206561279

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

6.744 × 10¹⁰²(103-digit number)

67440639685042186984…29218718501206561279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.744 × 10¹⁰²(103-digit number)

67440639685042186984…29218718501206561281

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

1.348 × 10¹⁰³(104-digit number)

13488127937008437396…58437437002413122559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.348 × 10¹⁰³(104-digit number)

13488127937008437396…58437437002413122561

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

2.697 × 10¹⁰³(104-digit number)

26976255874016874793…16874874004826245119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.697 × 10¹⁰³(104-digit number)

26976255874016874793…16874874004826245121

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

5.395 × 10¹⁰³(104-digit number)

53952511748033749587…33749748009652490239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.395 × 10¹⁰³(104-digit number)

53952511748033749587…33749748009652490241

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

1.079 × 10¹⁰⁴(105-digit number)

10790502349606749917…67499496019304980479

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

Block #237,542

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