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Block #347,004

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/6/2014, 9:43:52 PM Β· Difficulty 10.2376 Β· 6,478,122 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
59cd21b2b0b45b8c7db7fe258b5020bfeb1072a6895e26acaf9854081fc8eb9d
View on Chainz β†—

Height

#347,004

Difficulty

10.237638

Transactions

1

Size

202 B

Version

2

Bits

0a3cd5da

Nonce

41,250

Timestamp

1/6/2014, 9:43:52 PM

Confirmations

6,478,122

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

cdfb2c17e3560197798b895cb8241cd2da288ae4a98c155f2a796ec63184379e
Transactions (1)
Coinbasecdfb2c17e35601…796ec63184379e
1 in β†’ 1 out9.5300 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.410 Γ— 10⁹⁹(100-digit number)
14101564359973303635…70734774777294407679
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
1.410 Γ— 10⁹⁹(100-digit number)
14101564359973303635…70734774777294407679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.410 Γ— 10⁹⁹(100-digit number)
14101564359973303635…70734774777294407681
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
2.820 Γ— 10⁹⁹(100-digit number)
28203128719946607271…41469549554588815359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.820 Γ— 10⁹⁹(100-digit number)
28203128719946607271…41469549554588815361
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
5.640 Γ— 10⁹⁹(100-digit number)
56406257439893214542…82939099109177630719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.640 Γ— 10⁹⁹(100-digit number)
56406257439893214542…82939099109177630721
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
1.128 Γ— 10¹⁰⁰(101-digit number)
11281251487978642908…65878198218355261439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.128 Γ— 10¹⁰⁰(101-digit number)
11281251487978642908…65878198218355261441
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
2.256 Γ— 10¹⁰⁰(101-digit number)
22562502975957285816…31756396436710522879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.256 Γ— 10¹⁰⁰(101-digit number)
22562502975957285816…31756396436710522881
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
4.512 Γ— 10¹⁰⁰(101-digit number)
45125005951914571633…63512792873421045759
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:57,845,092 XPMΒ·at block #6,825,125 Β· updates every 60s
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