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Block #719,817

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2014, 2:58:16 AM Β· Difficulty 10.9509 Β· 6,096,707 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ca8ccc4a8308e20c075f525788495064f156d3651a6be6a7d57a1233545d60cd
View on Chainz β†—

Height

#719,817

Difficulty

10.950881

Transactions

3

Size

4.32 KB

Version

2

Bits

0af36cf4

Nonce

2,351,323,658

Timestamp

9/14/2014, 2:58:16 AM

Confirmations

6,096,707

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

27e52d386d71d6d9437c4bc9711f48f821a16ffd1e3a615d1228ff0c76ca93e1
Transactions (3)
Coinbase20cf78fbc5d367…088a66e089b47d
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
ff7653beec49dd…8e0a76ea89dd9f
1 in β†’ 2 out19999.9900 XPM226 B
AK2KG9rA…d97ADiTrAe48Evdk…86MndGHr
efcea3b28c55c4…113b77510dadfb
34 in β†’ 2 out334.1454 XPM3.90 KB
AbSr2HPU…JD3UCQJhAYzsMZt3…DmU2Unhv
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.

3.004 Γ— 10⁹⁴(95-digit number)
30041916460706915350…36706682017354692079
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
3.004 Γ— 10⁹⁴(95-digit number)
30041916460706915350…36706682017354692079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.004 Γ— 10⁹⁴(95-digit number)
30041916460706915350…36706682017354692081
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
6.008 Γ— 10⁹⁴(95-digit number)
60083832921413830701…73413364034709384159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.008 Γ— 10⁹⁴(95-digit number)
60083832921413830701…73413364034709384161
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
1.201 Γ— 10⁹⁡(96-digit number)
12016766584282766140…46826728069418768319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.201 Γ— 10⁹⁡(96-digit number)
12016766584282766140…46826728069418768321
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
2.403 Γ— 10⁹⁡(96-digit number)
24033533168565532280…93653456138837536639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.403 Γ— 10⁹⁡(96-digit number)
24033533168565532280…93653456138837536641
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
4.806 Γ— 10⁹⁡(96-digit number)
48067066337131064560…87306912277675073279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.806 Γ— 10⁹⁡(96-digit number)
48067066337131064560…87306912277675073281
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:57,776,318 XPMΒ·at block #6,816,523 Β· updates every 60s
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