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Block #654,099

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/29/2014, 11:39:12 PM Β· Difficulty 10.9552 Β· 6,149,684 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
747b4e9a53a98df624287380aa8883eae1fba118fab523fb2aceb180175c2b57
View on Chainz β†—

Height

#654,099

Difficulty

10.955204

Transactions

2

Size

72.84 KB

Version

2

Bits

0af48842

Nonce

91,761,897

Timestamp

7/29/2014, 11:39:12 PM

Confirmations

6,149,684

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4070982b014a57c43f6ca9dbf31dbc34a9fd2a32f02752e661501a3528e0c0d3
Transactions (2)
Coinbase6e106e30d7b209…67136fc18a1ed6
1 in β†’ 1 out9.0700 XPM116 B
ANSXnLY2…Sd25TjkD
a55af36822311e…613a114e86609a
502 in β†’ 2 out500.0100 XPM72.64 KB
AKgZmE3b…ZcpUdPmzAUE5QneS…bDZqwQ1J
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.

2.612 Γ— 10⁹⁡(96-digit number)
26120810587708001889…86548926528217843199
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
2.612 Γ— 10⁹⁡(96-digit number)
26120810587708001889…86548926528217843199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.612 Γ— 10⁹⁡(96-digit number)
26120810587708001889…86548926528217843201
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
5.224 Γ— 10⁹⁡(96-digit number)
52241621175416003778…73097853056435686399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.224 Γ— 10⁹⁡(96-digit number)
52241621175416003778…73097853056435686401
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
1.044 Γ— 10⁹⁢(97-digit number)
10448324235083200755…46195706112871372799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.044 Γ— 10⁹⁢(97-digit number)
10448324235083200755…46195706112871372801
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
2.089 Γ— 10⁹⁢(97-digit number)
20896648470166401511…92391412225742745599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.089 Γ— 10⁹⁢(97-digit number)
20896648470166401511…92391412225742745601
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
4.179 Γ— 10⁹⁢(97-digit number)
41793296940332803022…84782824451485491199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.179 Γ— 10⁹⁢(97-digit number)
41793296940332803022…84782824451485491201
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
8.358 Γ— 10⁹⁢(97-digit number)
83586593880665606045…69565648902970982399
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:57,674,304 XPMΒ·at block #6,803,782 Β· updates every 60s
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