Block #388,605

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/3/2014, 10:24:57 PM · Difficulty 10.4173 · 6,419,116 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4c2add684ef45b46a06f314df065af8c7405048660e59fe8a5039fc0ccf95f7

View on Chainz ↗

Height

#388,605

Difficulty

10.417295

Transactions

Size

1004 B

Version

Bits

0a6ad3d1

Nonce

1,633

Timestamp

2/3/2014, 10:24:57 PM

Confirmations

6,419,116

Mined by

⛏️ P2SHAQpbsNNXFUsJe8cy97ECCXAJ1mP4WVkPP2

Merkle Root

9005743f1afabd7bac4012d5ee7c22c7968d88e7d5ba9f8302a970dc0d3c1163

Transactions (5)

Coinbase564ca0cb1eb9e6…8eccdaf3c2b11f

1 in → 1 out9.2400 XPM111 B

AQpbsNNX…P4WVkPP2

06c0b227592573…18aa95bb1b3547

1 in → 1 out200.4880 XPM192 B

AUZimYhS…6jeBr98Z

c0d3f94d9ca728…50ea783f1c523d

1 in → 2 out34.6875 XPM225 B

AcrAXpZz…ihccxnk6 AYxzocSc…avKbLH2W

c2ce00313aa39b…96b33aec1427d4

1 in → 1 out2.9988 XPM191 B

AQNfg9Du…fk7MsSc7

5d3aa3539d9dc9…aafed4ee039f4b

1 in → 1 out2.9800 XPM193 B

APkdbNk6…tpPktux5

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.

4.031 × 10⁹⁹(100-digit number)

40316819170306067626…06512314423995022399

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

4.031 × 10⁹⁹(100-digit number)

40316819170306067626…06512314423995022399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.031 × 10⁹⁹(100-digit number)

40316819170306067626…06512314423995022401

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

8.063 × 10⁹⁹(100-digit number)

80633638340612135253…13024628847990044799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.063 × 10⁹⁹(100-digit number)

80633638340612135253…13024628847990044801

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

1.612 × 10¹⁰⁰(101-digit number)

16126727668122427050…26049257695980089599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.612 × 10¹⁰⁰(101-digit number)

16126727668122427050…26049257695980089601

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

3.225 × 10¹⁰⁰(101-digit number)

32253455336244854101…52098515391960179199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.225 × 10¹⁰⁰(101-digit number)

32253455336244854101…52098515391960179201

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

6.450 × 10¹⁰⁰(101-digit number)

64506910672489708202…04197030783920358399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.450 × 10¹⁰⁰(101-digit number)

64506910672489708202…04197030783920358401

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 #388,605

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