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Block #2,261,236

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/21/2017, 6:29:00 AM Β· Difficulty 10.9521 Β· 4,581,669 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8f8b2540a31c6668fc052bf93e57312d255252e9a7b74d510081bc986a49742d
View on Chainz β†—

Height

#2,261,236

Difficulty

10.952058

Transactions

2

Size

426 B

Version

2

Bits

0af3ba0e

Nonce

571,212,331

Timestamp

8/21/2017, 6:29:00 AM

Confirmations

4,581,669

Mined by

⛏️ P2SHAFrmAJ8ptbxzPJxPDo5UPEYyD8ihAyfkcU

Merkle Root

ce172c020ffcdf7ab7511ca3bf39903fd21b85f2059e3c4797b1b8bdfaa64613
Transactions (2)
Coinbase46edf7ff076239…b55ea4ec145df0
1 in β†’ 1 out8.3300 XPM110 B
AFrmAJ8p…ihAyfkcU
3b379de3c5f484…a175130f9bf20b
1 in β†’ 2 out146659.8823 XPM226 B
AViBaKwf…3Xk3qwK8Ae9xSynB…kB1xMWHN
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.

1.604 Γ— 10⁹⁴(95-digit number)
16047683608218683629…66590497222243085599
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
1.604 Γ— 10⁹⁴(95-digit number)
16047683608218683629…66590497222243085599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.604 Γ— 10⁹⁴(95-digit number)
16047683608218683629…66590497222243085601
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
3.209 Γ— 10⁹⁴(95-digit number)
32095367216437367258…33180994444486171199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.209 Γ— 10⁹⁴(95-digit number)
32095367216437367258…33180994444486171201
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
6.419 Γ— 10⁹⁴(95-digit number)
64190734432874734517…66361988888972342399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.419 Γ— 10⁹⁴(95-digit number)
64190734432874734517…66361988888972342401
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
1.283 Γ— 10⁹⁡(96-digit number)
12838146886574946903…32723977777944684799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.283 Γ— 10⁹⁡(96-digit number)
12838146886574946903…32723977777944684801
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
2.567 Γ— 10⁹⁡(96-digit number)
25676293773149893806…65447955555889369599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.567 Γ— 10⁹⁡(96-digit number)
25676293773149893806…65447955555889369601
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
5.135 Γ— 10⁹⁡(96-digit number)
51352587546299787613…30895911111778739199
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:57,987,587 XPMΒ·at block #6,842,904 Β· updates every 60s
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