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Block #714,273

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2014, 10:12:46 PM Β· Difficulty 10.9553 Β· 6,083,843 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2b7fd6f297838a5f53630e7e50929a79ec674bae3343746331d6bdcdf2c8ff51
View on Chainz β†—

Height

#714,273

Difficulty

10.955299

Transactions

1

Size

207 B

Version

2

Bits

0af48e7d

Nonce

986,280,212

Timestamp

9/9/2014, 10:12:46 PM

Confirmations

6,083,843

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c9a97f5ed51ed4f418cd8a3e678ab6c4ca925d70451d2b69f7d9ebe0249dbc78
Transactions (1)
Coinbasec9a97f5ed51ed4…d9ebe0249dbc78
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.660 Γ— 10⁹⁷(98-digit number)
26607813349110302568…87386154899748741119
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
2.660 Γ— 10⁹⁷(98-digit number)
26607813349110302568…87386154899748741119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.660 Γ— 10⁹⁷(98-digit number)
26607813349110302568…87386154899748741121
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
5.321 Γ— 10⁹⁷(98-digit number)
53215626698220605137…74772309799497482239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.321 Γ— 10⁹⁷(98-digit number)
53215626698220605137…74772309799497482241
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
1.064 Γ— 10⁹⁸(99-digit number)
10643125339644121027…49544619598994964479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.064 Γ— 10⁹⁸(99-digit number)
10643125339644121027…49544619598994964481
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
2.128 Γ— 10⁹⁸(99-digit number)
21286250679288242054…99089239197989928959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.128 Γ— 10⁹⁸(99-digit number)
21286250679288242054…99089239197989928961
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
4.257 Γ— 10⁹⁸(99-digit number)
42572501358576484109…98178478395979857919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.257 Γ— 10⁹⁸(99-digit number)
42572501358576484109…98178478395979857921
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:57,628,930 XPMΒ·at block #6,798,115 Β· updates every 60s
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