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Block #696,746

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2014, 11:20:16 AM Β· Difficulty 10.9583 Β· 6,108,463 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5344998fdcdc297611d9665f9cd6881981cd4fa0a62250b7bb5016d3438f4929
View on Chainz β†—

Height

#696,746

Difficulty

10.958260

Transactions

2

Size

1.14 KB

Version

2

Bits

0af55087

Nonce

513,400,560

Timestamp

8/28/2014, 11:20:16 AM

Confirmations

6,108,463

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

83e39d7db0ea22e04e83cab7cc49dc2d9130c434ef400990f691e728365a9f0f
Transactions (2)
Coinbase765ce14b25c2ed…cfa65a397df11c
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
fcdba3391e51ca…f9a073120ec22f
6 in β†’ 2 out42.0871 XPM966 B
AVACTrJz…3vm5pPx1AZak6L1V…Yz3nYfTo
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.

5.353 Γ— 10⁹⁴(95-digit number)
53533832804181377583…24650963712108200959
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
5.353 Γ— 10⁹⁴(95-digit number)
53533832804181377583…24650963712108200959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.353 Γ— 10⁹⁴(95-digit number)
53533832804181377583…24650963712108200961
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
1.070 Γ— 10⁹⁡(96-digit number)
10706766560836275516…49301927424216401919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.070 Γ— 10⁹⁡(96-digit number)
10706766560836275516…49301927424216401921
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
2.141 Γ— 10⁹⁡(96-digit number)
21413533121672551033…98603854848432803839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.141 Γ— 10⁹⁡(96-digit number)
21413533121672551033…98603854848432803841
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
4.282 Γ— 10⁹⁡(96-digit number)
42827066243345102066…97207709696865607679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.282 Γ— 10⁹⁡(96-digit number)
42827066243345102066…97207709696865607681
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
8.565 Γ— 10⁹⁡(96-digit number)
85654132486690204133…94415419393731215359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.565 Γ— 10⁹⁡(96-digit number)
85654132486690204133…94415419393731215361
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
1.713 Γ— 10⁹⁢(97-digit number)
17130826497338040826…88830838787462430719
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:57,685,744 XPMΒ·at block #6,805,208 Β· updates every 60s
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