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Block #685,307

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/20/2014, 4:43:39 PM Β· Difficulty 10.9558 Β· 6,113,987 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
75650ae39c6c651464354550dd2a427cf957d221aaaf69202ab5c66390017498
View on Chainz β†—

Height

#685,307

Difficulty

10.955833

Transactions

2

Size

2.30 KB

Version

2

Bits

0af4b175

Nonce

423,596,951

Timestamp

8/20/2014, 4:43:39 PM

Confirmations

6,113,987

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

573763b33c322e80a273ef939797f909c06246ea1cd775bd105712770bf32356
Transactions (2)
Coinbaseedc65f62164bf2…ceed090baf18c4
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
1032bc1e0f9c5b…32ed690df97727
14 in β†’ 2 out1.2676 XPM2.10 KB
AdQzAsNH…HGN6kTzUAPWh6XEv…WNRBH3WL
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.

9.800 Γ— 10⁹⁢(97-digit number)
98002999809098144987…78815260266972828159
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
9.800 Γ— 10⁹⁢(97-digit number)
98002999809098144987…78815260266972828159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.800 Γ— 10⁹⁢(97-digit number)
98002999809098144987…78815260266972828161
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
1.960 Γ— 10⁹⁷(98-digit number)
19600599961819628997…57630520533945656319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.960 Γ— 10⁹⁷(98-digit number)
19600599961819628997…57630520533945656321
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
3.920 Γ— 10⁹⁷(98-digit number)
39201199923639257994…15261041067891312639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.920 Γ— 10⁹⁷(98-digit number)
39201199923639257994…15261041067891312641
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
7.840 Γ— 10⁹⁷(98-digit number)
78402399847278515989…30522082135782625279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.840 Γ— 10⁹⁷(98-digit number)
78402399847278515989…30522082135782625281
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
1.568 Γ— 10⁹⁸(99-digit number)
15680479969455703197…61044164271565250559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.568 Γ— 10⁹⁸(99-digit number)
15680479969455703197…61044164271565250561
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:57,638,396 XPMΒ·at block #6,799,293 Β· updates every 60s
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