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Block #2,127,848

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/22/2017, 7:15:15 AM Β· Difficulty 10.9178 Β· 4,714,615 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5f7bc755d6f865468470214d65038aa5e1a33b85e5885ea83f02a5a5b392b63a
View on Chainz β†—

Height

#2,127,848

Difficulty

10.917842

Transactions

1

Size

200 B

Version

2

Bits

0aeaf7ae

Nonce

209,757,059

Timestamp

5/22/2017, 7:15:15 AM

Confirmations

4,714,615

Mined by

⛏️ P2SHAc2bN6be4tcAb6AjaUsE75gW4vb2wyC9GL

Merkle Root

72f8a89bd049d1c46db1d488a3ac3c5f6f0dd7060dff1a2585fb8f6aadfa522d
Transactions (1)
Coinbase72f8a89bd049d1…fb8f6aadfa522d
1 in β†’ 1 out8.3800 XPM110 B
Ac2bN6be…b2wyC9GL
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.

3.013 Γ— 10⁹⁡(96-digit number)
30135626272680323874…87053062150672243199
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
3.013 Γ— 10⁹⁡(96-digit number)
30135626272680323874…87053062150672243199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.013 Γ— 10⁹⁡(96-digit number)
30135626272680323874…87053062150672243201
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
6.027 Γ— 10⁹⁡(96-digit number)
60271252545360647749…74106124301344486399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.027 Γ— 10⁹⁡(96-digit number)
60271252545360647749…74106124301344486401
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
1.205 Γ— 10⁹⁢(97-digit number)
12054250509072129549…48212248602688972799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.205 Γ— 10⁹⁢(97-digit number)
12054250509072129549…48212248602688972801
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
2.410 Γ— 10⁹⁢(97-digit number)
24108501018144259099…96424497205377945599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.410 Γ— 10⁹⁢(97-digit number)
24108501018144259099…96424497205377945601
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
4.821 Γ— 10⁹⁢(97-digit number)
48217002036288518199…92848994410755891199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.821 Γ— 10⁹⁢(97-digit number)
48217002036288518199…92848994410755891201
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
9.643 Γ— 10⁹⁢(97-digit number)
96434004072577036398…85697988821511782399
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:57,984,122 XPMΒ·at block #6,842,462 Β· updates every 60s
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