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Block #716,685

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2014, 8:06:22 PM Β· Difficulty 10.9523 Β· 6,079,432 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
929bcfee482fef16a0063501571166a278798cde077d1e2af2ca355fce140bbd
View on Chainz β†—

Height

#716,685

Difficulty

10.952318

Transactions

2

Size

401 B

Version

2

Bits

0af3cb20

Nonce

2,014,609,165

Timestamp

9/11/2014, 8:06:22 PM

Confirmations

6,079,432

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

abdaa8528b3791eb0783407ff2644746ccc869a368b4a2d436e20d62a71cf5f5
Transactions (2)
Coinbase67f4ed60c3a70b…fd44e302899e30
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
1aff4e1530f562…20ec81eb6a74f8
1 in β†’ 2 out8.3100 XPM193 B
AeKNrjNj…1NEq95TaAM6JvF6Y…u5DULnSo
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.

8.554 Γ— 10⁹⁸(99-digit number)
85544309306619261656…32281390369819033599
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
8.554 Γ— 10⁹⁸(99-digit number)
85544309306619261656…32281390369819033599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.554 Γ— 10⁹⁸(99-digit number)
85544309306619261656…32281390369819033601
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
1.710 Γ— 10⁹⁹(100-digit number)
17108861861323852331…64562780739638067199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.710 Γ— 10⁹⁹(100-digit number)
17108861861323852331…64562780739638067201
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
3.421 Γ— 10⁹⁹(100-digit number)
34217723722647704662…29125561479276134399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.421 Γ— 10⁹⁹(100-digit number)
34217723722647704662…29125561479276134401
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
6.843 Γ— 10⁹⁹(100-digit number)
68435447445295409325…58251122958552268799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.843 Γ— 10⁹⁹(100-digit number)
68435447445295409325…58251122958552268801
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
1.368 Γ— 10¹⁰⁰(101-digit number)
13687089489059081865…16502245917104537599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.368 Γ— 10¹⁰⁰(101-digit number)
13687089489059081865…16502245917104537601
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:57,612,932 XPMΒ·at block #6,796,116 Β· updates every 60s
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