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Block #551,871

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/19/2014, 2:51:09 AM Β· Difficulty 10.9624 Β· 6,264,584 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9c3aad83d6c7623eca3390a1978b4e8f532ba5e737abe3c7cd60e87ac4bfcdc7
View on Chainz β†—

Height

#551,871

Difficulty

10.962415

Transactions

1

Size

243 B

Version

2

Bits

0af660d7

Nonce

3,576,775

Timestamp

5/19/2014, 2:51:09 AM

Confirmations

6,264,584

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

96674ee1368ff36cae2515f0204c93cb83d25b47a2066127886d0fed8e57d397
Transactions (1)
Coinbase96674ee1368ff3…6d0fed8e57d397
1 in β†’ 2 out8.3100 XPM152 B
ARzmpY4c…fvx8bF9tALPu3s2c…EJXLjVFh
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.137 Γ— 10⁹⁷(98-digit number)
51378659525657331453…78118296705852868579
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.137 Γ— 10⁹⁷(98-digit number)
51378659525657331453…78118296705852868579
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.137 Γ— 10⁹⁷(98-digit number)
51378659525657331453…78118296705852868581
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.027 Γ— 10⁹⁸(99-digit number)
10275731905131466290…56236593411705737159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.027 Γ— 10⁹⁸(99-digit number)
10275731905131466290…56236593411705737161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.055 Γ— 10⁹⁸(99-digit number)
20551463810262932581…12473186823411474319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.055 Γ— 10⁹⁸(99-digit number)
20551463810262932581…12473186823411474321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.110 Γ— 10⁹⁸(99-digit number)
41102927620525865162…24946373646822948639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.110 Γ— 10⁹⁸(99-digit number)
41102927620525865162…24946373646822948641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
8.220 Γ— 10⁹⁸(99-digit number)
82205855241051730325…49892747293645897279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.220 Γ— 10⁹⁸(99-digit number)
82205855241051730325…49892747293645897281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.644 Γ— 10⁹⁹(100-digit number)
16441171048210346065…99785494587291794559
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,775,767 XPMΒ·at block #6,816,454 Β· updates every 60s
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