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Block #708,550

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2014, 6:26:41 PM Β· Difficulty 10.9575 Β· 6,088,290 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
65e87e75a9f6d4c21a7970f558961a3186f92c1ac3fa5ad048efa5f6ecb84e78
View on Chainz β†—

Height

#708,550

Difficulty

10.957475

Transactions

2

Size

697 B

Version

2

Bits

0af51d15

Nonce

3,226,554,068

Timestamp

9/5/2014, 6:26:41 PM

Confirmations

6,088,290

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f54595bcc969af3bbff2914377d0a05c241163b08b24a07618fc64e103de1703
Transactions (2)
Coinbase66c5e9d096eecb…761abd3bdfa7bd
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
0de89fd3b93fd9…c23c8be641987f
3 in β†’ 1 out3.2747 XPM489 B
AJqgK1v7…jhVYUMAr
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.

3.276 Γ— 10⁹⁹(100-digit number)
32764678872429824744…33089161139186237439
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
3.276 Γ— 10⁹⁹(100-digit number)
32764678872429824744…33089161139186237439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.276 Γ— 10⁹⁹(100-digit number)
32764678872429824744…33089161139186237441
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
6.552 Γ— 10⁹⁹(100-digit number)
65529357744859649489…66178322278372474879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.552 Γ— 10⁹⁹(100-digit number)
65529357744859649489…66178322278372474881
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
1.310 Γ— 10¹⁰⁰(101-digit number)
13105871548971929897…32356644556744949759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.310 Γ— 10¹⁰⁰(101-digit number)
13105871548971929897…32356644556744949761
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
2.621 Γ— 10¹⁰⁰(101-digit number)
26211743097943859795…64713289113489899519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.621 Γ— 10¹⁰⁰(101-digit number)
26211743097943859795…64713289113489899521
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
5.242 Γ— 10¹⁰⁰(101-digit number)
52423486195887719591…29426578226979799039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.242 Γ— 10¹⁰⁰(101-digit number)
52423486195887719591…29426578226979799041
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:57,618,732 XPMΒ·at block #6,796,839 Β· updates every 60s
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