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Block #928,619

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/9/2015, 5:55:09 AM Β· Difficulty 10.9035 Β· 5,881,234 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a63055585c080ebcdb6c71551d8462b92e424ee5e0a0104ca8afb07912b73de
View on Chainz β†—

Height

#928,619

Difficulty

10.903501

Transactions

2

Size

991 B

Version

2

Bits

0ae74bdb

Nonce

1,079,307,281

Timestamp

2/9/2015, 5:55:09 AM

Confirmations

5,881,234

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

443f912bc9d8fc9b00ebc9cbfdab80f14eeab2118aac056974066416c41fcd4d
Transactions (2)
Coinbasee1453dc5e95bf7…6a2e2ddcf3a88d
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
46d133a8c2b1d0…491917b744168d
5 in β†’ 1 out26.4468 XPM785 B
AWF4rtPp…LnbQHVaN
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.

8.022 Γ— 10⁹⁴(95-digit number)
80228896187160784474…67769926927754298599
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
8.022 Γ— 10⁹⁴(95-digit number)
80228896187160784474…67769926927754298599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.022 Γ— 10⁹⁴(95-digit number)
80228896187160784474…67769926927754298601
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
1.604 Γ— 10⁹⁡(96-digit number)
16045779237432156894…35539853855508597199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.604 Γ— 10⁹⁡(96-digit number)
16045779237432156894…35539853855508597201
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
3.209 Γ— 10⁹⁡(96-digit number)
32091558474864313789…71079707711017194399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.209 Γ— 10⁹⁡(96-digit number)
32091558474864313789…71079707711017194401
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
6.418 Γ— 10⁹⁡(96-digit number)
64183116949728627579…42159415422034388799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.418 Γ— 10⁹⁡(96-digit number)
64183116949728627579…42159415422034388801
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
1.283 Γ— 10⁹⁢(97-digit number)
12836623389945725515…84318830844068777599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.283 Γ— 10⁹⁢(97-digit number)
12836623389945725515…84318830844068777601
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:57,722,911 XPMΒ·at block #6,809,852 Β· updates every 60s
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