Block #617,028

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/4/2014, 7:31:11 PM · Difficulty 10.9458 · 6,193,953 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33fdf2ac5d8a75010a65033a9f45c12bae185e3aad0ef9018747345aa62c6ccf

View on Chainz ↗

Height

#617,028

Difficulty

10.945792

Transactions

Size

1.23 KB

Version

Bits

0af21f65

Nonce

130,487,680

Timestamp

7/4/2014, 7:31:11 PM

Confirmations

6,193,953

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9b9765e9428aac9750b7ac4a9ff8043709d845f34ecc20ad93e82248dd61e4a1

Transactions (5)

Coinbase214df99344ce73…d647427150c3ce

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

120283a7274a0a…45c0980fe56df8

2 in → 2 out10.1503 XPM374 B

APU4tXUv…G9cGMteH Ae2KcfvC…Y5z6Ufi7

4541002f9d8803…075fb089f36719

1 in → 2 out7.8298 XPM226 B

AH2GA673…zMhfwK7A AYH2n5Dg…4QUxzaYS

4730229840b37c…a5685f678added

1 in → 2 out7.3101 XPM226 B

AWxT75KZ…iSQdqTBw AXourZrA…u89738dP

65617a79f167ed…1ec9364735a335

1 in → 2 out7.2738 XPM227 B

AKtTxBvw…YQXMRNHp AYz8XXeX…wUExhw54

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.

4.107 × 10⁹⁶(97-digit number)

41070778568791653474…36124995025319497519

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

4.107 × 10⁹⁶(97-digit number)

41070778568791653474…36124995025319497519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.107 × 10⁹⁶(97-digit number)

41070778568791653474…36124995025319497521

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

8.214 × 10⁹⁶(97-digit number)

82141557137583306949…72249990050638995039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.214 × 10⁹⁶(97-digit number)

82141557137583306949…72249990050638995041

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

1.642 × 10⁹⁷(98-digit number)

16428311427516661389…44499980101277990079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.642 × 10⁹⁷(98-digit number)

16428311427516661389…44499980101277990081

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

3.285 × 10⁹⁷(98-digit number)

32856622855033322779…88999960202555980159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.285 × 10⁹⁷(98-digit number)

32856622855033322779…88999960202555980161

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

6.571 × 10⁹⁷(98-digit number)

65713245710066645559…77999920405111960319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.571 × 10⁹⁷(98-digit number)

65713245710066645559…77999920405111960321

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

1.314 × 10⁹⁸(99-digit number)

13142649142013329111…55999840810223920639

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 #617,028

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