Block #591,918

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/17/2014, 10:59:40 AM · Difficulty 10.9438 · 6,224,739 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb12c9fb12b16b9e9009147557ba66a65ff9a0287c833dc57e77f805065148c0

View on Chainz ↗

Height

#591,918

Difficulty

10.943805

Transactions

Size

10.11 KB

Version

Bits

0af19d3a

Nonce

940,729,056

Timestamp

6/17/2014, 10:59:40 AM

Confirmations

6,224,739

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cef7fa56281b9459f3e44e6626ebc2dc8f184a60d5bf99f29a5aad2c0206c113

Transactions (4)

Coinbasec49dc97a13198d…8684d5d1a6ef52

1 in → 1 out8.4600 XPM116 B

ANSXnLY2…Sd25TjkD

bc2d005d6b5b72…ee8aaef8a97c94

65 in → 2 out500.0101 XPM9.47 KB

AG8x1Lgk…mGrL1WKG AJjnK9uC…VreFquR4

7fbea2e055ef78…57d199d03aaeef

1 in → 2 out0.7601 XPM225 B

Ace6jQFL…7s5BouRF AGdWVjRk…LFVsqCnK

d2d6fc862b2584…9ab0b194d23266

1 in → 2 out0.6942 XPM227 B

AbA1925a…X3QKnaUJ ASkuboV8…mBQxNm3J

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.

2.027 × 10⁹⁷(98-digit number)

20274120967945439853…35897274170675942619

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

2.027 × 10⁹⁷(98-digit number)

20274120967945439853…35897274170675942619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.027 × 10⁹⁷(98-digit number)

20274120967945439853…35897274170675942621

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

4.054 × 10⁹⁷(98-digit number)

40548241935890879706…71794548341351885239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.054 × 10⁹⁷(98-digit number)

40548241935890879706…71794548341351885241

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

8.109 × 10⁹⁷(98-digit number)

81096483871781759412…43589096682703770479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.109 × 10⁹⁷(98-digit number)

81096483871781759412…43589096682703770481

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

1.621 × 10⁹⁸(99-digit number)

16219296774356351882…87178193365407540959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.621 × 10⁹⁸(99-digit number)

16219296774356351882…87178193365407540961

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

3.243 × 10⁹⁸(99-digit number)

32438593548712703765…74356386730815081919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.243 × 10⁹⁸(99-digit number)

32438593548712703765…74356386730815081921

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

6.487 × 10⁹⁸(99-digit number)

64877187097425407530…48712773461630163839

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 #591,918

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