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Block #2,655,629

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/10/2018, 8:28:20 AM Β· Difficulty 11.7037 Β· 4,181,254 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
56e978265ecce9393e5a07d790fde3d400ca9ba20130260f9e6820fa0386145e
View on Chainz β†—

Height

#2,655,629

Difficulty

11.703731

Transactions

2

Size

572 B

Version

2

Bits

0bb427b3

Nonce

455,128,757

Timestamp

5/10/2018, 8:28:20 AM

Confirmations

4,181,254

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

c51dcd80bb1a86509683261aae3b849c31d03bdf21c8f32f3701116c6d4e4333
Transactions (2)
Coinbasee15f8c02bd59b7…b46a9574d6b72e
1 in β†’ 1 out7.3000 XPM110 B
Adqah8zh…1WwoHJ9t
4117dc3c460118…4270a0a6ea6547
2 in β†’ 2 out270.5893 XPM372 B
AKf74TEF…iNryuktPAKDCJWi1…fgY2eZQt
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.

9.886 Γ— 10⁹⁴(95-digit number)
98863939092270552486…71561866102258555839
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
9.886 Γ— 10⁹⁴(95-digit number)
98863939092270552486…71561866102258555839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.886 Γ— 10⁹⁴(95-digit number)
98863939092270552486…71561866102258555841
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
1.977 Γ— 10⁹⁡(96-digit number)
19772787818454110497…43123732204517111679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.977 Γ— 10⁹⁡(96-digit number)
19772787818454110497…43123732204517111681
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
3.954 Γ— 10⁹⁡(96-digit number)
39545575636908220994…86247464409034223359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.954 Γ— 10⁹⁡(96-digit number)
39545575636908220994…86247464409034223361
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
7.909 Γ— 10⁹⁡(96-digit number)
79091151273816441989…72494928818068446719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.909 Γ— 10⁹⁡(96-digit number)
79091151273816441989…72494928818068446721
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
1.581 Γ— 10⁹⁢(97-digit number)
15818230254763288397…44989857636136893439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.581 Γ— 10⁹⁢(97-digit number)
15818230254763288397…44989857636136893441
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
3.163 Γ— 10⁹⁢(97-digit number)
31636460509526576795…89979715272273786879
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:57,939,356 XPMΒ·at block #6,836,882 Β· updates every 60s
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