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Block #2,252,070

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2017, 3:13:10 AM Β· Difficulty 10.9485 Β· 4,590,377 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0fe938f2ec438816981f0edec7bc361a2f5e63ac36f822eb397b89313bb981b4
View on Chainz β†—

Height

#2,252,070

Difficulty

10.948507

Transactions

1

Size

200 B

Version

2

Bits

0af2d15b

Nonce

949,074,415

Timestamp

8/15/2017, 3:13:10 AM

Confirmations

4,590,377

Mined by

⛏️ P2SHAWhpQuwA2hWFiwtUwmV8brp21aDwTkKeMY

Merkle Root

1e4bc843b2a5e0216448246a6c2fb038139707255b525a94a999ee7d59f59e8d
Transactions (1)
Coinbase1e4bc843b2a5e0…99ee7d59f59e8d
1 in β†’ 1 out8.3300 XPM110 B
AWhpQuwA…DwTkKeMY
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.

4.181 Γ— 10⁹⁡(96-digit number)
41815314940894941717…02690598889102795199
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
4.181 Γ— 10⁹⁡(96-digit number)
41815314940894941717…02690598889102795199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.181 Γ— 10⁹⁡(96-digit number)
41815314940894941717…02690598889102795201
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
8.363 Γ— 10⁹⁡(96-digit number)
83630629881789883435…05381197778205590399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.363 Γ— 10⁹⁡(96-digit number)
83630629881789883435…05381197778205590401
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
1.672 Γ— 10⁹⁢(97-digit number)
16726125976357976687…10762395556411180799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.672 Γ— 10⁹⁢(97-digit number)
16726125976357976687…10762395556411180801
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
3.345 Γ— 10⁹⁢(97-digit number)
33452251952715953374…21524791112822361599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.345 Γ— 10⁹⁢(97-digit number)
33452251952715953374…21524791112822361601
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
6.690 Γ— 10⁹⁢(97-digit number)
66904503905431906748…43049582225644723199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.690 Γ— 10⁹⁢(97-digit number)
66904503905431906748…43049582225644723201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,983,993 XPMΒ·at block #6,842,446 Β· updates every 60s
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