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Block #2,273,812

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2017, 8:14:51 PM Β· Difficulty 10.9546 Β· 4,565,360 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ecfbbf930c3707a508853a87533a138fa56ad75cf0656b349c1c36ec6150dac
View on Chainz β†—

Height

#2,273,812

Difficulty

10.954564

Transactions

2

Size

427 B

Version

2

Bits

0af45e51

Nonce

99,117,044

Timestamp

8/29/2017, 8:14:51 PM

Confirmations

4,565,360

Mined by

⛏️ P2SHAbA6Wb2wcTAEStfynLJRWUa6BSucE3kfny

Merkle Root

52f542cbbd21a337459edb0db996574d26298ae583585c7bb0dcd50299dd3f7e
Transactions (2)
Coinbasedd21350f811061…95a67153c8a5b6
1 in β†’ 1 out8.3300 XPM110 B
AbA6Wb2w…ucE3kfny
9e5d16f0caef69…242a5a233c6c14
1 in β†’ 2 out2562.3518 XPM226 B
ASaVFj36…BGC6cTS2AN8ChhTf…8rbdSVLi
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.

7.932 Γ— 10⁹⁷(98-digit number)
79321229025829870786…44915802279498137599
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
7.932 Γ— 10⁹⁷(98-digit number)
79321229025829870786…44915802279498137599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.932 Γ— 10⁹⁷(98-digit number)
79321229025829870786…44915802279498137601
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
1.586 Γ— 10⁹⁸(99-digit number)
15864245805165974157…89831604558996275199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.586 Γ— 10⁹⁸(99-digit number)
15864245805165974157…89831604558996275201
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
3.172 Γ— 10⁹⁸(99-digit number)
31728491610331948314…79663209117992550399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.172 Γ— 10⁹⁸(99-digit number)
31728491610331948314…79663209117992550401
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
6.345 Γ— 10⁹⁸(99-digit number)
63456983220663896629…59326418235985100799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.345 Γ— 10⁹⁸(99-digit number)
63456983220663896629…59326418235985100801
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
1.269 Γ— 10⁹⁹(100-digit number)
12691396644132779325…18652836471970201599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.269 Γ— 10⁹⁹(100-digit number)
12691396644132779325…18652836471970201601
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
2.538 Γ— 10⁹⁹(100-digit number)
25382793288265558651…37305672943940403199
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:57,957,657 XPMΒ·at block #6,839,171 Β· updates every 60s
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