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Block #1,507,658

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/22/2016, 1:36:28 PM Β· Difficulty 10.6249 Β· 5,308,967 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
98077c4e3ae1befe00f23bfa9a7bc801e98475fd07eea81313fe436d7484242d
View on Chainz β†—

Height

#1,507,658

Difficulty

10.624924

Transactions

2

Size

10.94 KB

Version

2

Bits

0a9ffafe

Nonce

197,883,321

Timestamp

3/22/2016, 1:36:28 PM

Confirmations

5,308,967

Mined by

⛏️ P2SHAakdvsD2V89WjHAgPqkd2fLnStz7jSxR12

Merkle Root

f9ffd8e42e019534bc0fdd535a9add6110574e5fea1ec3751a3148a75dbd346e
Transactions (2)
Coinbasea8254656b3dbe7…cbf414d9b1b250
1 in β†’ 1 out9.3800 XPM109 B
AakdvsD2…z7jSxR12
4d7887fbce1c0e…f04a70854735d4
74 in β†’ 1 out27.0000 XPM10.74 KB
AW9z6iyE…ZMok5rfx
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.

1.282 Γ— 10⁹⁡(96-digit number)
12820729958025460215…60192424590948710399
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
1.282 Γ— 10⁹⁡(96-digit number)
12820729958025460215…60192424590948710399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.282 Γ— 10⁹⁡(96-digit number)
12820729958025460215…60192424590948710401
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
2.564 Γ— 10⁹⁡(96-digit number)
25641459916050920431…20384849181897420799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.564 Γ— 10⁹⁡(96-digit number)
25641459916050920431…20384849181897420801
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
5.128 Γ— 10⁹⁡(96-digit number)
51282919832101840863…40769698363794841599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.128 Γ— 10⁹⁡(96-digit number)
51282919832101840863…40769698363794841601
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
1.025 Γ— 10⁹⁢(97-digit number)
10256583966420368172…81539396727589683199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.025 Γ— 10⁹⁢(97-digit number)
10256583966420368172…81539396727589683201
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
2.051 Γ— 10⁹⁢(97-digit number)
20513167932840736345…63078793455179366399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.051 Γ— 10⁹⁢(97-digit number)
20513167932840736345…63078793455179366401
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:57,777,123 XPMΒ·at block #6,816,624 Β· updates every 60s
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