Block #508,480

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/24/2014, 10:20:26 AM · Difficulty 10.8184 · 6,296,683 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4488fc837c4c2a4079635f717f150c1522c908e943f6e589f1d9da4c810e4450

View on Chainz ↗

Height

#508,480

Difficulty

10.818393

Transactions

Size

1.08 KB

Version

Bits

0ad18238

Nonce

967,117

Timestamp

4/24/2014, 10:20:26 AM

Confirmations

6,296,683

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

edd7291eeb3c15f12e5a936bf6dc001203a5e587b94d348eedd3903bdb17f19e

Transactions (5)

Coinbase7de2a1533f4861…a647e2aac3df5a

1 in → 1 out8.5700 XPM110 B

AeKNrjNj…1NEq95Ta

03c13f270b9c51…e99bc930b0700a

1 in → 2 out6.4670 XPM226 B

AGpvdZiL…yRF55qor AUhgi2TK…5yKhLLXx

e74d829cb77f03…39df3c20ad54df

1 in → 2 out4.1509 XPM225 B

AZBBbBQf…F3kFciBH AWZu9NdF…Ndqn9mP5

d44fbdbf4aaf5c…9c8ed02ec47f46

1 in → 2 out5.7265 XPM226 B

AVSTjM25…912zpK9m AeHmxERP…2hhYf2ho

b1aee8a70d45cd…bb225c50b4ba53

1 in → 2 out2.7949 XPM226 B

Af2zhzpV…ABbCdJRJ ANZMnGxv…bDfTYi5m

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.570 × 10¹⁰⁰(101-digit number)

35705512439222900425…70692529700879016959

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

3.570 × 10¹⁰⁰(101-digit number)

35705512439222900425…70692529700879016959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.570 × 10¹⁰⁰(101-digit number)

35705512439222900425…70692529700879016961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.141 × 10¹⁰⁰(101-digit number)

71411024878445800851…41385059401758033919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.141 × 10¹⁰⁰(101-digit number)

71411024878445800851…41385059401758033921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.428 × 10¹⁰¹(102-digit number)

14282204975689160170…82770118803516067839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.428 × 10¹⁰¹(102-digit number)

14282204975689160170…82770118803516067841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.856 × 10¹⁰¹(102-digit number)

28564409951378320340…65540237607032135679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.856 × 10¹⁰¹(102-digit number)

28564409951378320340…65540237607032135681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.712 × 10¹⁰¹(102-digit number)

57128819902756640681…31080475214064271359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.712 × 10¹⁰¹(102-digit number)

57128819902756640681…31080475214064271361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer